# Harold Edwards (mathematician)

**Harold Mortimer Edwards, Jr.** (born August 6, 1936) is an American mathematician working in number theory, algebra, and the history and philosophy of mathematics.

Harold Mortimer Edwards, Jr. | |
---|---|

Born | |

Nationality | American |

Alma mater | Harvard University |

Awards | Leroy P. Steele Prize |

Scientific career | |

Fields | Mathematics |

Institutions | New York University |

Doctoral advisor | Raoul Bott |

He was one of the co-founding editors, with Bruce Chandler, of *The Mathematical Intelligencer*.[1]
He is the author of expository books on the Riemann zeta function, on Galois theory, and on Fermat's Last Theorem. He wrote a book on Leopold Kronecker's work on divisor theory providing a systematic exposition of that work—a task that Kronecker never completed. He has written textbooks on linear algebra, calculus, and number theory. He also wrote a book of essays on constructive mathematics.

## Biography

Edwards received his Ph.D. in 1961 from Harvard University, under the supervision of Raoul Bott.[2] He has taught at Harvard and Columbia University; he joined the faculty at New York University in 1966, and has been an emeritus professor since 2002.[1]

In 1980, Edwards won the Leroy P. Steele Prize for Mathematical Exposition of the American Mathematical Society, for his books on the Riemann zeta function and Fermat's Last Theorem.[3] For his contribution in the field of the history of mathematics he was awarded the Albert Leon Whiteman Memorial Prize by the AMS in 2005.[4] In 2012 he became a fellow of the American Mathematical Society.[5]

Edwards is married to Betty Rollin, a former NBC News correspondent, author, and breast cancer survivor.[6]

## Books

*Higher Arithmetic: An Algorithmic Introduction to Number Theory*(2008)[7]

An extension of Edwards' work in*Essays in Constructive Mathematics*, this textbook covers the material of a typical undergraduate number theory course,[8] but follows a constructivist viewpoint in focusing on algorithms for solving problems rather than allowing purely existential solutions.[8][9] The constructions are intended to be simple and straightforward, rather than efficient, so, unlike works on algorithmic number theory, there is no analysis of how efficient they are in terms of their running time.[9]*Essays in Constructive Mathematics*(2005)[10]

Although motivated in part by the history and philosophy of mathematics, the main goal of this book is to show that advanced mathematics such as the fundamental theorem of algebra, the theory of binary quadratic forms, and the Riemann–Roch theorem can be handled in a constructivist framework.[11][12][13]*Linear Algebra*, Birkhäuser, (1995)*Divisor Theory*(1990)[14]

Algebraic divisors were introduced by Kronecker as an alternative to the theory of ideals.[15] According to the citation for Edwards' Whiteman Prize, this book completes the work of Kronecker by providing "the sort of systematic and coherent exposition of divisor theory that Kronecker himself was never able to achieve."[4]*Galois Theory*(1984)[16]

Galois theory is the study of the solutions of polynomial equations using abstract symmetry groups. This book puts the origins of the theory into their proper historical perspective, and carefully explains the mathematics in Évariste Galois' original manuscript (reproduced in translation).[17][18]

Mathematician Peter M. Neumann won the Lester R. Ford Award of the Mathematical Association of America in 1987 for his review of this book.[19]*Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory*(1977)[20]

As the word "genetic" in the title implies, this book on Fermat's Last Theorem is organized in terms of the origins and historical development of the subject. It was written some years prior to Wiles' proof of the theorem, and covers research related to the theorem only up to the work of Ernst Kummer, who used p-adic numbers and ideal theory to prove the theorem for a large class of exponents, the regular primes.[21][22]*Riemann's Zeta Function*(1974)[23]

This book concerns the Riemann zeta function and the Riemann hypothesis on the location of the zeros of this function. It includes a translation of Riemann's original paper on these subjects, and analyzes this paper in depth; it also covers methods of computing the function such as Euler–Maclaurin summation and the Riemann–Siegel formula. However, it omits related research on other zeta functions with analogous properties to Riemann's function, as well as more recent work on the large sieve and density estimates.[24][25][26]*Advanced Calculus: A Differential Forms Approach*(1969)[27]

This textbook uses differential forms as a unifying approach to multivariate calculus. Most chapters are self-contained. As an aid to learning the material, several important tools such as the implicit function theorem are described first in the simplified setting of affine maps before being extended to differentiable maps.[28][29]

## See also

## References

- Curriculum vitae from Edwards' web site at NYU, retrieved 2010-01-30.
- Harold Mortimer Edwards, Jr. at the Mathematics Genealogy Project.
- Leroy P. Steel Prizes, American Mathematical Society, retrieved 2010-01-31.
- "2005 Whiteman Prize" (PDF),
*Notices of the AMS*,**52**(4), April 2005. - List of Fellows of the American Mathematical Society, retrieved 2012-12-02.
- Klemesrud, Judy (September 9, 1985), "Daughter's Story: Aiding Mother's Suicide",
*New York Times*. - American Mathematical Society, 2008, ISBN 978-0-8218-4439-7.
- Review by Samuel S. Wagstaff, Jr. (2009),
*Mathematical Reviews*, MR2392541. - Review by Luiz Henrique de Figueiredo, Mathematical Association of America, April 26, 2008.
- Springer-Verlag, 2005, ISBN 0-387-21978-1.
- Schulman, Bonnie (February 22, 2005), "Essays in Constructive Mathematics by Harold M. Edwards",
*Read This! The MAA Online book review column*, Mathematical Association of America. - Review by Edward J. Barbeau (2005),
*Mathematical Reviews*, MR2104015. - Review by S. C. Coutinho (2010),
*SIGACT News***41**(2): 33–36, doi:10.1145/1814370.1814372. - Birkhäuser, 1990, ISBN 0-8176-3448-7.
- Review by D. Ştefănescu (1993),
*Mathematical Reviews*, MR1200892. - Graduate Texts in Mathematics 101, Springer-Verlag, 1984, ISBN 0-387-90980-X.
- Review by B. Heinrich Matzat (1987),
*Mathematical Reviews*, MR0743418. - Review by Peter M. Neumann (1987),
*American Mathematical Monthly***93**: 407–411. - The Lester R. Ford Award, MAA, retrieved 2010-02-01.
- Graduate Texts in Mathematics 50, Springer-Verlag, New York, 1977, ISBN 0-387-90230-9. Reprinted with corrections, 1996, ISBN 978-0-387-95002-0, MR1416327. Russian translation by V. L. Kalinin and A. I. Skopin. Mir, Moscow, 1980, MR0616636.
- Review by Charles J. Parry (1981),
*Bulletin of the AMS***4**(2): 218–222. - Review by William C. Waterhouse (1983),
*Mathematical Reviews*, MR0616635. - Pure and Applied Mathematics 58, Academic Press, 1974. Republished by Dover Publications, 2001, ISBN 978-0-486-41740-0.
- Review by Harvey Cohn (1975),
*SIAM Review***17**(4): 697–699, doi:10.1137/1017086. - Review by Robert Spira (1976),
*Historia Mathematica***3**(4): 489–490, doi:10.1016/0315-0860(76)90087-2. - Review by Bruce C. Berndt,
*Mathematical Reviews*, MR0466039. - Houghton–Mifflin, 1969. Reprinted with corrections by Krieger Publishing, 1980. Republished again by Birkhäuser, 1993, ISBN 0-8176-3707-9.
- Review by Nick Lord (1996),
*The Mathematical Gazette***80**(489): 629–630, doi:10.2307/3618555. - Review by R. S. Booth (1982),
*Mathematical Reviews*, MR0587115.